hi im still new and need a few questions cleared up as to how BTC's are generated. I mean I keep reading about mining bitcoins, but in my head it just seems like leaving the computer on for SETI and looking for alien life. That I can understand, but bitcoins I dont understand why these codes have to be generated to then be used. Why can we just generate them with a click of a button?

Every time some solves a Block it's 50 coins to the group of the individual that solves it. Solving a block confirms transactions. So in a way its how Bitcoin prints and distributes money.

It solving an algorithm. You don't get a block if it can't be confirmed. I doubt anyone has close to enough power to break SHA-256 encryption and "make their own bitcoins". If they did there would be a lot more issues then counterfeiting of bitcoins.